DEARBORN, Mich. — Ford will update software on 2013 Escapes and Fusions to stop their engines from overheating, a problem that has caused a small number of fires.

Reports of nine fires prompted the automaker to recall more than 89,000 of the SUVs and mid-size cars in the United States and Canada last month. No injuries were reported, and only models with 1.6-liter turbocharged engines were recalled.

Ford offered free loaner cars until it figured out what caused the fires.

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It was the fourth recall in four months for the new ­Escape, a top seller in the competitive market for small SUVs. The 2013 version has had problems with coolant leaks, cracked fuel lines, and carpet padding since it started selling this spring. The Fusion has been recalled twice.

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The overheating problem occurs when coolant does not flow through the radiator to be cooled, Ford Motor Co.’s product development chief, Raj Nair, said Monday. Engineers found that a valve that controls the flow of coolant wasn’t opening at the right time.

A software change will solve the problem, Nair said.

The software updates should be available at dealers early next week, Nair said.

Because the problem is so rare, the cars and SUVs are safe to drive. But if drivers see a warning light about overheating, they should pull to the side of the road, shut down the engine, and call a dealer, Nair said.